I have some suggestions, for readability and simplicity.
With utility scripts like this, I find putting the usage at the top of the code, reminds me what this is SUPPOSED to do. &usage is cool , but you can do similarly and IMHO easier as....
my $usage=<<EOF;
usage:
These are your options punk.
EOF

die $usage unless ($#ARGV==3);

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Also , pretty sure you could use map to replace the core searcher. 
print OUTFILE map { /$phrase/ && $_}  <INFILE>;

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Which might reduce the number of operations you need for each match, rather than a while - if arrangement.

In reply to Re: compressed logfile grep by submersible_toaster
in thread compressed logfile grep by ibanix

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